Generalized Lorenz–Mie scattering theory for focused radiation and finite solids of revolution: case I: symmetrically polarized beams

Abstract

Interaction of focused radiation with spherical and finite cylindrical homogeneous particles is considered. The aim of this investigation is to calculate the structure of the electromagnetic (EM) fields scattered by and propagated within the scattering objects. The incident EM fields are assumed to be focused fields in the image space of an aplanatic system with or without aberrations of category one. The radiation in the object space is assumed to be symmetrically polarized. The incident fields in the neighbourhood of the focus are calculated using the well-known theory of Richards and Wolf and a methodology developed by the author. At the interface between the homogeneous and the image space of the aplanatic system, the continuity conditions of the tangential components of the electric displacement and magnetic moment vectors are satisfied. The procedure results in dual discretized-Fredholm integral equations that are solved using orthogonal expansions. It is assumed that the scattered field, at large distances from the focus, is a spherical wave propagating away from the focus. Scattering by objects of various materials ranging from dielectric to perfect conductor is studied. The theory and its solution developed here allow for the scattering objects to be located anywhere along the optical axis in the image space. One of the main objectives is to calculate the energy distribution at the tip of the cylindrical homogeneous particle. Numerical calculations suggest that energy density at the tip is further enhanced if the cylindrical homogeneous particle is placed away from focus.